Theory Weekly Highlights for January through June 2004
Highlights for June 2004
Ideal calculations for a sequence of fully bootstrapped equilibria obtained by scaling the vacuum toroidal field showed instability with no wall but stability with the DIII-D wall and with considerable structure in the growth rates as functions of q_0, q min, and q_edge. Minima and maxima in the growth rates do not correspond to integer values of any of q_0, q_min, and q_edge. The perturbed flux on the outer, low field side boundary is also remarkably insensitive to these parameters over a wide range (5 5 < q_0 < 12.05), including the successive maxima and minima in the growth rate. The outboard mode structure is insensitive to the q_edge value even though the poloidal m = n* q_edge harmonic (n = 1) dominates at the boundary, and is even insensitive to he presence or absence of nearby integer q_edge values where there is a strong peeling component. This result implies that active feedback control of the associated RWM should also be quite insensitive to these parameters, which may simplify feedback schemes.
Based on the assumption that the angular momentum confinement time is the same as the energy confinement time, a formula has been devised for the toroidal rotation frequency expected in ITER. This projects a 2.4 kHz rotation frequency for ITER, given an efficiency of 50% for generating toroidal momentum from a 1 MeV neutral beam. The method also predicts a 21 kHz rotation rate for DIII-D, which is of the order that is generally observed. This should be extremely useful in ITER design work, especially for Resistive Wall Mode stabilization.
Recent modeling has shown that, given sufficient pulse length, a steady state ITER configuration is achievable assuming the GLF23 energy and toroidal rotation transport model and fixed density profiles. The simulations were based on current 9-MA discharge ITER design parameters and used the ONETWO transport code, together with ECH and ECCD calculations from TORAY-GA and fast wave ICH and ICCD from CURRAY. The steady state configuration features a constant E parallel, with essentially 100% non-inductive current drive, and is maintained by a total of 73MW of input power, consisting of 33MW of 1MeV NNBI, 20 MW of fast wave and 20 MW of ECH. Optimization of the non-inductive current fraction and fusion gain assuming the initial ITER hardware capabilities is underway.
Highlights for May 2004
A new gyro-Landau fluid (GLF) system of moment equations that includes both trapped and passing particles, covering both electrons and ions has been completed. This unified model has been a long-sought goal. For each species, the new GLF system has twelve moments for passing and three for trapped particles, but in the absence of trapped particles, reduces to the six-moment Beer and Hammett equations. The system is solved as an eigenmode problem and can resolve subdominant instabilities not found by an initial value calculation; the eigenmode solution is no more expensive near threshold and is faster than existing initial value gyro-kinetic linear stability codes. The model has been tested for wavenumbers from the lowest trapped ion range to the highest electron temperature gradient mode. Benchmark scans over subsets of a large database of gyro-kinetic linear stability calculations find growth rate and frequency standard deviations typically about 10%. The new model has wide application as a data analysis tool and will be incorporated in a successor to the GLF23 transport model.
In an external initiative to test the scalability of the new vector architecture Cray X1 supercomputer, GYRO was run on a temporarily configured X1 with 504 Multi-Streaming Processors (MSPs). Using the full machine, a GYRO benchmark case was run showing very good scalability and a step time of 0.07s. The same case was tested on the IBM Power3 at NERSC using up to 2688 processors, with the best step time of 0.41s at 1792 processors. Thus, the Cray exceeded the peak IBM performance by a factor of 6 using 3.5 times fewer processors. This is very good news for Cray and clearly highlights the effectiveness of their new vector architecture for our compute-intensive simulation problems.
In new work on pellet fueling of tokamak plasmas, it was shown that injection through a guide tube that is bent through 90 degrees can still deliver the pellet largely intact, though strongly deformed into a long pencil-shape. Normally, the tubes used to guide pellets from the low field side to their injection point at the high-field point, as called for in the ITER design, must bend through a considerable angle to achieve the desired trajectories normal to the magnetic surface. It was found that an initial right-cylinder pellet of volume �a3/4, deforms into an object of length (= a(R/a)2/5 and diameter r=a(a/R)1/5 upon executing a 90� guide tube bend. Here R denotes the radius of curvature. This result depends on the validity of the fluid model, which is generally well satisfied, and is independent of pellet velocity. For ITER parameters, ( = 4.8 cm and r = 0.45 cm when a=1cm and R= 50 cm. Future work will focus on the ablation of such pencil-thin pellets from the high field side.
Torkil Jensen died peacefully on May 1 2004 after a long battle with cancer, and ended a long, productive, and uniquely innovative career at General Atomics and DIII-D spanning almost 50 years. His humanity, his wonderfully playful sense of humor, and, of course, his famous Limericks, will be deeply missed. He contributed this highlight:
The Highlightwriter's Plight
Each Friday he turns on his lights
To search for spectacular sights
Of new innovations
And mental gestations
Each week he will aim for new heights
T. Jensen.
Highlights for April 2004
The latest version TORAY-GA1.7 is ready for public release. Dimensions of both equilibrium and radial grid point arrays are now allocated automatically and the different common block files previously needed to run with different resolution are now replaced by a single file. TORAY-GA1.7 was validated to test its robustness and reproducibility across platforms. The test cases include comparisons of the absorbed power and driven current profiles for different launch locations, harmonic, X-mode or O-mode waves, different damping and current drive modules, and varying equilibrium and profile resolution. Within reasonable accuracy, the code gives the same results on both Linux (gemini) and HP (hydra) systems and interacts correctly with other codes, ONETWO, CQL3D, and GAFIT for each test case. This validation work is summarized in a file "Doc_toray1.7.doc" in the CVS directory.
The Linux cluster that performs between-shot EFIT, CER analysis and profile fitting analysis has been upgraded. It now has 12 dual-Xeon 2.66 MHz processors. The cluster can now complete a typical magnetic EFIT calculation in 30 seconds, including data retrieval, which is about half of the time that the previous cluster took. Whereas the old cluster was running at full capacity during operations, with the new cluster, significantly more analyses can be added between shots, such as map_to_rho and spectrometry analysis. Kinetic EFIT and power balance analysis an also potentially be included.
Nonlinear extended MHD simulations of ELMs with NIMROD have shown an energy distribution in the mode structure peaked at low and high mode numbers. Low n modes initially have a lower linear growth rate compared to higher n. Assuming equipartition of energy in the toroidal modes as an initial condition, preliminary results indicate that the higher n modes grow linearly to large amplitude and their beating nonlinearly drives the lower n modes to large amplitude. Intermediate n=5-10 modes are robustly linearly unstable but are not strongly driven by the higher n modes in the early nonlinear phase. The coupled modes form complex structures in flow velocity and temperature; high temperature areas are seen flowing out with vortices clearly evident, in agreement with other models. The temperature and flow structures are antisymmetric above and below the midplane. The simulations cannot yet be continued late into the nonlinear phase due to the need for higher toroidal mode resolution; presently up to n = 21 is included. Although inclusion of higher modes will almost certainly change some results significantly, the bipolar energy distribution is expected to remain in the early nonlinear phase, since it is driven by the nearest-neighbor beating process.
See also http://fusion.gat.com/theory/NIMROD_ELM_simulations for details.
A new, web-based, video conferencing software for audio and video broadcasting, VRVS, has been set up to make DIII-D operations widely available for remote participation. Both DIII-D operations and the 8:05AM pre-operation meeting are being broadcasted via dedicated "DIII-D Virtual Room". Currently, there are three video streams from the control room and one video stream from the building 34 conference room available. The audio is the combination of physics operator audio, session leader audio, and pre-operation meeting room audio. A controllable, web-based, high-resolution camera is also installed in the DIII-D control room. As a result, DIII-D researchers and collaborators can now participate remotely in DIII-D experiments and the pre-operation meetings using their office desktop computer.
Investigations into the ideal MHD stability of tokamaks with a current hole region, lead to the conclusion that their stability can be treated as a plasma with two 'vacuum like' regions. For perturbations with finite toroidal mode number, the current hole region behaves exactly like a vacuum region. This is consistent with standard tokamak external kink analyses where the stability of a vacuum and a current free and pressure gradient free plasma are identical when there are no rational surfaces in the region. For axisymmetric perturbations, however, the analysis is more subtle. In that case, the minimizing perturbation consists of the superposition of three different kinds of independent displacements: a vertical displacement, which does not contribute to the stabilization of the plasma, and two other displacements that compress the plasma and the toroidal magnetic field respectively. These are non-negative definite so cannot provide any destabilization. However, we have not yet been able to prove that these contributions can be made to vanish for the minimizing perturbation.
Highlights for March 2004
A new variation of the model for mass shedding due to magnetic shear induced differential drift of a pellet cloud has been implemented in the Pressure Relaxation Lagrangian (PRL) code. This code calculates the fast inward MHD drift and fuel deposition profile of pellet ablation material following HFS pellet injection. The code has also been coupled with the PELLET code to initialize the cloud parameters along the ablation track. Penetration calculations were done with temperature profiles having a tanh function pedestal, where the pedestal height is defined as the inflection point. The resulting deposition profiles for a 6mm pellet injected into an ITER-like Te profile (To=20kev, Tped = 4 kev and pedestal width = 8.5 cm), are significantly different for pellets with velocities of 300 and 1000 m/s, but there is little difference between pellets with velocities of 1000 and 1500 m/s. The conventional, curved guide tube, ITER injection scheme limits pellet speeds to 300 m/s, but the PELLET code predicts that these pellets will burn out in the pedestal region, and this degrades subsequent MHD penetration of the ablated and ionized material. Parameter scans and sensitivity tests for the temperature and q profile are underway to confirm if this holds universally.
GYRO simulations motivated by SciDAC benchmarking efforts have revealed several encouraging general results. Global GYRO simulations yield transport coefficients that agree in the limit of small gyroradius to system size, with local (flux-tube) turbulence simulations from the GS2 and PG3EQ codes. This firmly establishes the "local hypothesis" which forms the basis of the GLF23 transport modeling code. However, the GTC results, which originally popularized this case, do not satisfy the local hypothesis. In addition, very-long-time GYRO flux-tube simulations (10x the usual simulation time, or about 10ms of a DIII-D discharge) have verified that the turbulence achieves a true statistical steady state; this validates the use of a time-dependent turbulence simulation to determine time-independent transport coefficients.
The algorithm to extract the coefficients of the large and small Frobenius solutions in the TWIST-R linear resistive stability code was successfully adapted from the original 1D version to the 2D toroidal case. The ratio of the leading small and large Frobenius components for the odd and even parity solutions yields the tearing and interchange stability indices Delta' and Gamma'. The 2D case has the additional complication that the solution contains a regular component in addition to the two Frobenius components that must be carefully extracted to reveal the subdominant small solution accurately. In a sample test case, mocking a solution for a 2D Solovev equilibrium, the coefficients of the small solution were extracted to sufficient accuracy on a moderate radial grid. For the more difficult situations that TWIST-R is designed to handle with the Mercier index mu > 1, the small solution is buried below two terms of the large and regular solutions each. However, the same accuracy should be recovered by simply doubling the mesh size.
The ONETWO suite of codes was installed at ORNL on the RANIER computer. This provides additional, badly needed, computing power to analyze Advanced Tokamak current drive scenarios using the computationally demanding GLF23 transport model. Results from these calculations were recently presented at the DIII-D PAC meeting. Of particular value is the ability to model steady state current drive situations using the nonlinear solution methods recently introduced into ONETWO; these increase the efficiency an order of magnitude by solving directly for the steady state solution without having to evolve through intermediate time steps. The RANIER system is presently being used for steady state ITER-FEAT modeling and the combination of the additional computing resources and nonlinear methods reduces meaningful current drive studies using the GLF23 model from the order of days to a more feasible several hours.
Highlights for February 2004
Calculations using the MARS-F code have revealed a synergistic effect between active feedback and rotational stabilization of the resistive wall mode (RWM) with the feedback coil located outside the plasma chamber. This synergistic stabilization is most effective when the growth rate of the RWM, gamma, has been slowed by rotation to a sufficiently low value of gamma*tau_w < 3, where tau_w is the flux diffusion time constant of the resistive wall. At that time the feedback gain required for stabilization is reduced considerably. This synergistic effect may be utilized advantageously in future devices such as ITER where plasma rotation by itself may not be sufficient to stabilize the RWM.
The theory developed for the onset and early evolution of tearing modes in high beta sawtoothing discharges in DIII-D appears to be valid in Alcator C-mod as well. Extensive nonlinear simulations of the seeding mechanism for DIII-D previously established the crucial role of evolving the linear stability in addition to modeling the nonlinear drive in the neoclassical island evolution. Preliminary analyses of equilibrium reconstructions from a similar Alcator C-mod experiment are consistent with the importance of both the classical linear and the nonlinear coupling drive to the tearing mode onset and early evolution, even though the sawtooth physics and neoclassical drive are expected to be different from that in DIII-D. The theory predicts that the details of the sawtooth physics and neoclassical drive are not important in determining the relative amplitude of the nonlinear drive to the early island evolution. This relative amplitude appears to be consistent with the theory in both experiments.
Previous theories of transport barrier formation have put forward the idea that a radial region that contains a minimum-q (zero shear) point is favorable to the formation of an ion transport barrier. However, studies of reversed shear plasmas using the GYRO code show, on the contrary, that there is no transport suppression in such a minimum-q region. These simulations indicate that the appearance of non-resonant ITG modes, which are neglected in the barrier formation theories, ensure that transport remains smooth across the point where shear vanishes. This result implies that theories of ITB formation that invoke special gyrokinetic effects at zero shear can be discounted; one needs to look at non-gyrokinetic explanations.
MDSplus data from 2003 was migrated from the old RAID array to the new Atlas server. The long-term plan is to replace the old RAID array with a new mass storage system, at which time all MDSplus data will be served from the new Atlas server the new Atlas server serves data faster than the old system.
Summary data from DIII-D discharge 70200 to the present were loaded into the DIII-D Relational Database (D3DRDB). These data values include scalars that summarize the characteristics of each discharge. A list of quantities in the summaries table is available at:
Highlights for January 2004
A re-analysis of published simulation predictions for the early MHD bursts in the Beta_N = 2 L-Mode NCS discharge 87009, has shown that many of the predictions are exhibited in more recent, lower Beta_N L-Mode NCS discharges. These were not previously understood or observed in discharge #87009. In both the simulations from the NFTC and FAR codes and the experimental data, the initially localized resistive interchange mode at the inner rational surface broadens until it reaches the magnetic axis. It then reconnects either at or just off-axis, consistent with a double tearing structure in which the innermost island is weaker than the outer island. The inner island then dissipates forming a single tearing mode. In the original simulations, the tearing was partly successful in explaining the Beta limit disruption. In the lower Beta_N experiments, however, the modified profiles lead simply to a loss of high performance, which is more consiste
Disclaimer
These highlights are reports of research work in progress and are accordingly subject to change or modification
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